Bounds on the number of vertices of perturbed polyhedra

Paul Armand (1)

1 LACO - Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation

Finding the incident edges to a degenerate vertex of a polyhedron is a non-trivial problem. So pivoting methods generally involve a perturbation argument to overcome the degeneracy problem. But the perturbation entails a bursting of each degenerate vertex into a cluster of nondegenerate vertices. The aim of this paper is to give some bounds on the number of these perturbed vertices.

Mots clés: Convex polytopes; degeneracy; linear programming; simplex method

Domaines: Mathématiques [math]

Paul Armand. Bounds on the number of vertices of perturbed polyhedra. Annals of Operations Research, 1993, 47, pp.249-269. ⟨10.1007/BF02023098⟩. ⟨hal-00110668⟩